What is the integral of 4xcos(-2x+5) ?

The integral of 4xcos(-2x+5) is -2xsin(-2x+5)+cos(-2x+5)+C

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integral of 4xcos(-2x+5)

\int 4 x cos (- 2 x + 5) d x

- 2 x sin (- 2 x + 5) + cos (- 2 x + 5) + C

Solution steps

\int 4 x cos (- 2 x + 5) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 4 \cdot \int x cos (- 2 x + 5) d x

Apply Integration By Parts

= 4 (- \frac{1}{2} x sin (- 2 x + 5) - \int - \frac{1}{2} sin (- 2 x + 5) d x)

\int - \frac{1}{2} sin (- 2 x + 5) d x = - \frac{1}{4} cos (- 2 x + 5)

= 4 (- \frac{1}{2} x sin (- 2 x + 5) - (- \frac{1}{4} cos (- 2 x + 5)))

Simplify

4 (- \frac{1}{2} x sin (- 2 x + 5) - (- \frac{1}{4} cos (- 2 x + 5))) : - 2 x sin (- 2 x + 5) + cos (- 2 x + 5)

= - 2 x sin (- 2 x + 5) + cos (- 2 x + 5)

Add a constant to the solution

= - 2 x sin (- 2 x + 5) + cos (- 2 x + 5) + C

What is the integral of 4xcos(-2x+5) ?
The integral of 4xcos(-2x+5) is -2xsin(-2x+5)+cos(-2x+5)+C